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2016 OIM Problems/Problem 6

Problem

Let $k$ be a positive integer and $a_1, a_2, \cdots a_k$ be digits. Prove that a positive integer $n$ exists such that the last $2k$ digits of $2^n$ are in this order, $a_1, a_2, \cdots, a_k, b_1, b_2, \cdots, b_k$, for certain digits $b_1, b_2, \cdots, b_k$

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions

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